• Korean Journal of Mathematics
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• v.18 no.3
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• pp.311-322
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• 2010

In this paper, we prove stabilities of the reciprocal difference functional equation $$r(\frac{x+y+z}{3})-r(x+y+z)=\frac{2r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ and the reciprocal adjoint functional equation $$r(\frac{x+y+z}{3})+r(x+y+z)=\frac{4r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ with three variables. Stabilities of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables was proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar. We extend their results to three variables in similar types.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.1
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• pp.49-56
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• 2002

The Z-map is a special farm of discrete non-parametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[ij]. While the z-map is the simplest farm of representing sculptured surfaces and is the most versatile scheme for modeling non-parametric objects, its practical application in industry (eg, tool-path generation) has aroused much controversy over its weaknesses, namely its inaccuracy, singularity (eg, vertical wall), and some excessive storage needs. Much research or the application of the z-map can be found in various articles, however, research on the systematic analysis of sculptured surface shape representation via the z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) z-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary z-map models, and some application examples.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.867-876
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• 2016

The object of the present paper is to investigate the starlikeness of the class of functions $f(z)=z^p+{\sum\limits_{k=n}^{\infty}}a_p+k^{z^{p^{+k}}} (p,n{\in}{\mathbb{N}}=\{1,2,{\ldots}\})$ which are analytic and p-valent in the unit disc U and satisfy the condition $\|(1-{\lambda}({\frac{f(z)}{z^p}})^{\alpha}+{\lambda}{\frac{zf^{\prime}(z)}{pf(z)}}({\frac{f(z)}{z^p}})^{\alpha}-1\|$ < ${\mu}$ (0 < ${\mu}{\leq}1$, ${\lambda}{\geq}0$, ${\alpha}$ > 0, $z{\in}U$). The starlikeness of certain integral operator are also discussed. The results obtained generalize the related works of some authors and some other new results are also obtained.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.147-154
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• 1988

For a positive integer p, $A_p$ will denote the class of functions $f(z)=z^p+\sum\limits^{\infty}_{n=p+1}a_nz^n$ which are analytic in the unit disc U = {z: |z| <1}. For $0{\leq}{\alpha}{\leq}1$, 0<${\beta}{\leq}1$, $0{\leq}{\lambda}$ $S_p({\alpha},{\beta},{\lambda})$ denote the class of functions $f(z){\in}A_p$ which satisfy the condition $\left|\frac{{\frac{zf^{\prime}(z)}{f(z)}}-p}{{{\alpha}{\frac{zf^{\prime}(z)}{f(z)}}+p-{\lambda}(1+{\alpha})}}\right|$<${\beta}$ for $z{\in}U$ In this paper we obtain a representation theorem for the class $S_p({\alpha},{\beta},{\lambda})$ and also derive distortion theorem and sharp estimates for the coefficients of this class.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.11
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• pp.180-188
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• 1998

Z-map is a special form of discrete nonparametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[i.j]. While z-map is the simplest form of representing sculptured surfaces and it is the most versatile scheme for modeling nonparametric objects, its practical application in industry (eg, tool-path generation) aroused much controversy over its weaknesses ; accuracy, singularity (eg, vertical wall), and some excessive storage needs. Although z-map has such limitations, much research on the application of z-map can be found in various articles. However, research on the systematic analysis of sculptured surface shape representation via z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) B-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary B-map models, and some application examples.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.855-868
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• 2021

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≤ 1, then for 𝜌R ≥ k² and 𝜌 ≤ R, Aziz and Zargar [4] proved that $${\max_{{\mid}z{\mid}=1}}{\mid}p^{\prime}(z){\mid}{\geq}n{\frac{(R+k)^{n-1}}{({\rho}+k)^n}}\{{\max_{{\mid}z{\mid}=1}}{\mid}p(z){\mid}+{\min_{{\mid}z{\mid}=k}}{\mid}p(z){\mid}\}$$. We prove a generalized L^r extension of the above result for a more general class of polynomials $p(z)=a_nz^n+\sum\limits_{{\nu}={\mu}}^{n}a_n-_{\nu}z^{n-\nu}$, $1{\leq}{\mu}{\leq}n$. We also obtain another L^r analogue of a result for the above general class of polynomials proved by Chanam and Dewan [6].

• Journal of Veterinary Clinics
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• v.12 no.1
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• pp.799-818
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• 1995

This study was performed to examine the general anesthetic efficacy of tiletamine-zolazepam, a mixture of phencyclidine-derived tiletamine and benzodiazepine-related zolazepam. The antagonistic activities of doxapram and yohimbine to the anesthetic effects of tiletamine-zolazepam were also studied. Thirty healthy mongrel dogs were divided into three groups (each of 10) twenty minutes after being anesthetized with tiletamine-zolazepam : T-Z-S group(tiletamine-zolazepam-saline), T-Z-D group (tiletamine -zolazepam-doxapram), T-Z-Y group (tiletamine-zolaz.pam-yohim bine). Various parameters wert evaluated in terms of the onset and recovery time of analgesia, respiration rates, hear rates, body temperature, electrocardiogram, blood chemistry, and lymphocyte blastogenesis. The results obtained through these experiment could be summarized as follows: 1. he anesthetic efficacy of tiletamine-zolazepam was considered desirable, with the onset time of anesthesia being as short as 0.23-0.24 minutes. 2. Both of the antagonistic effects of yohimbine and doxapram on the anesthesia induced by liletamine-zolazepan were evaluated statistically significant(p<0.05) as the recovery time was shortened from 39.3$\pm$4.9 min(T-Z-S group) to 25.3$\pm$2.9 nin(T-Z-Y group) and 29.9$\pm$8.8min(T-Z-D group), respectively. 3. Respiration rates were not changed by the treatments of both doxapram and yohimbine, with the only transient increase in the T-Z-D group. The changes in the respiration rate were not observed during the whole time course of the experiment. 4. Yohimbine(T-Z-Y group) increased the heart rate significantly from 30 minutes after the adminstration compared to the T-Z-S group and T-Z-D group (p<0.05). 5. The decreases in th, body temporature were observed from 30 minutes in the T-Z-S group(p<0.05) and 40 minutes in th, T-Z-D group(p<0.05), after the adminstration. On the other hand, there was no hypothermia in the T-Z-Y group. 6. In the all experimental groups of the T-Z-S, T-Z-D and T-Z-Y, there were no specific findings on the electrocardiograph incept slight shift to the tachycardia in all cases. 1. We could not find any differences in the blood chemistry between all experimental groups (T-Z-S, T-Z-D and T-Z-Y). 8. the inhibition of the lymphocyte blastogenesis shown in the T-Z-S with 3 hours decreasing and thereafter restoring to the normal values up to the point 5 hours were not occurred in the T-Z-D and T-Z-Y groups. With the above results, we could conclude that both doxapram and yohimbine can be clinically used as recovery agents towards anesthesia by tiletamine- zolazepam fi:on the efficacy point of view, but yohimbine is more recommendable in this case if considering the recovery time and lymphocyte blastogenesis.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.5
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• pp.668-676
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• 2003

The effect of nozzle height on heat transfer of a hot steel plate cooled by an impinging liquid jet is not well understood. Previous studies have been based on the dimensionless parameter z/d. To test the validity of this dimensionless parameter and to investigate gravitational effects on the jet, stagnation velocity of an impinging liquid jet were measured and the cooling experiments of a hot steel plate were conducted for z/d from 6.7 to 75, and an inverse heat conduction method is applied for the quantitative comparison. Also, the critical instability point of a liquid jet was examined over a range of flow rates. The experimental velocity data for the liquid jet were well correlated with the dimensionless number 1/F $r_{z}$$^2$based on distance. It was thought that the z/d parameter was not valid for heat transfer to an impinging liquid jet under gravitational forces. In the cooling experiments, heat transfer was independent of z when 1/F $r_{z}$$^2$< 0.187(z/d = 6.7). However, it was found that the heat transfer quantity for 1/F $r_{z}$$^2$=0.523(z/d = 70) is larger 11% than that in the region for 1/F $r_{z}$$^2$=0.187. The discrepancy between these results and previous research is likely due to the instability of liquid jet.uid jet.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.507-518
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• 2020

We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by 𝒩. For the function f(z) = z + a₂z² + a₃z³ + … which is defined in the unit disc D such that the function f(z) belongs to the class 𝒩, we estimate from below the modulus of the angular derivative of the function ${\frac{f{^{\prime}^{\prime}}(z)}{f(z)}}$ at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].